(1 point) prove the following statement: if a e z and n e n, then gcd(a, a + n)|n. proof: let gcd(a, a n) = d. this implies that and therefore for some y e z. for some x e z and e z. therefore since x, y e z, therefore thus n= о. е. d.

Paula makes stained-glass windows and sells them to boutique stores. if her costs total $12,000 per year plus $4 per window for the frame. how many windows must she produce to earn a profit of at least $48,000 in one year if she sells the windows for $28 each? 1. define a variable for the situation. 2. write an inequality that represents her profit. note: revenue is money coming in. cost is money going out. profit is the difference between the revenue and the cost. in other words: revenue - costs profit 3.using words, describe how many windows she must sell to have a profit of at least $48,000.